Unwanted UV Vertices
To get even texture pattern I think the seams on the mug indeed should be re-arranged.

That "vertice" in the original UV map actually represents all the inner faces of the mug together with mug's handle. That's why the model should be unwrapped and so the seams can be put in this way:

 

In this example the seams are placed on:


The outer mesh handle's loopcut; it starts on the bottom of it outside and ends on the bottom inside.
The inner mesh handle's loopcut.
The loopcut opposite the mug' handle.
The very top loopcut of the mesh (inner one, so as not to be seen from the outside).


After some UV map tweaking (scaling loopcuts so the shape to be more quad-like and without distortions) and arranging islands, it can look like this:



Note: if texture on the bottom of the mesh will be seen somehow, then topology there should be rebuilt.

Thus the texture on your mug will be placed in this way:



Blend file